A257521 Odd Brazilian numbers.

7, 13, 15, 21, 27, 31, 33, 35, 39, 43, 45, 51, 55, 57, 63, 65, 69, 73, 75, 77, 81, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 121, 123, 125, 127, 129, 133, 135, 141, 143, 145, 147, 153, 155, 157, 159, 161, 165, 171, 175, 177, 183, 185, 187, 189, 195

Offset

1,1

Comments

All even integers 2p >=8 are Brazilian numbers (A125134), because 2p=2(p-1)+2 is written 22 in base p-1 if p-1>2, that is true if p >=4. But, among Brazilian numbers, there are also odd ones...

The only square of a prime is 121. - Robert G. Wilson v, May 21 2015

Links

Daniel Lignon and Robert Israel, Table of n, a(n) for n = 1..10000 (first 703 from Daniel Lignon)

Maple

N:= 1000: # to get all terms <= N
for b from 2 to floor(N/2-1) do
   dk:= 1 + (b mod 2);
   for j from 1 to b-1 by 2 do
     for k from dk by dk do
       if j=1 and k=1 then next fi;
       x:= j*(b^(k+1)-1)/(b-1);
       if x > N then break fi;
       B[x]:= 1;
     od
   od
od:
sort(map(op, [indices(B)])); # Robert Israel, May 27 2015

Mathematica

fQ[n_] := Block[{b = 2}, While[b < n - 1 && Length[ Union[ IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; Select[1 + 2 Range@100, fQ] (* Robert G. Wilson v, May 21 2015 *)

Prog

(PARI) forstep(n=5, 300, 2, for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), print1(n, ", "); break))) \\ Derek Orr, Apr 30 2015

Crossrefs

Cf. A125134 (Brazilian numbers), A253261 (odd Brazilian squares).

Cf. A085104 (prime Brazilian numbers).

Sequence in context: A349752 A167782 A326380 * A053696 A090503 A059520

Adjacent sequences: A257518 A257519 A257520 * A257522 A257523 A257524

Keyword

nonn,base,easy

Author

Daniel Lignon, Apr 27 2015

Status

approved